A picture is hung from a nail with wire. The nail supports two forces A = 5.0N and B =
5.0N.
1. Draw a free body diagram of the nail, illustrating the x and y components of
vector A and B. (Solve for component forces with a precision of 0.0)
2. Calculate the x and y components of the resultant force (R) by summing the x
and y components of vectors A and B.
ΣFx = FAx + FBx
ΣFx = -2.5N + 2.5N = 0
ΣFy = FAy +FBy
ΣFy = -4.3N + -4.3N = -8.6 N
An eye screw is experiencing two tension forces G 100N and
H 50N.
3. Sketch vector G with its x and y components. (Solve
for component forces with a precision of 0.0)
4. Sketch vector G with its x and y components. (Solve for component forces with
a precision of 0.0)
5. Calculate the sum of the x and y components of vectors G and H. (precision of
0.0)
ΣFx = FGx + FHx
ΣFy = FGy + FHy
46.98 N + 25.88 N = 72.86 N = 72.9 N
17.1 N + 96.59 N = 113.69 N = 113.7 N
6. If you know the components of a vector, what mathematical relationship can be
used to find the magnitude of the vector?
2
2
2
Pythagorean Theorem, 𝑎 + 𝑏 = 𝑐 . Since the vector components are at
right angles to each other, they are the legs of a right triangle, lengths and b
in the Pythagorean Theorem, and the hypotenuse is the resultant. c in the
Pythagorean theorem is the magnitude of that resultant.
7. Sketch the resultant force (R) and calculate the magnitude and angle of the
vector.